Abstract: Cross-efficiency evaluation, as an extension tool of data envelopment analysis(DEA), has been widely applied in evaluating and ranking decision making units(DMUs). Unfortunately, the baleful evaluation among peers makes the efficiency valued impractical. In this paper, the third party is regarded as an indirect element. Considering that these indirect elements are transitive in the efficiency evaluation matrix, the indirect judgment results are introduced to iterate the original cross-efficiency matrix repeatedly, and the final stability of the iteration process is proved. Finally a numerical example shows the applications and flexibility of the model in this paper.

Key words: efficiency evaluation matrix, transitive closure matrix, fuzzy operator

摘要： 现有交叉效率矩阵中往往会存在一些同行效率评价远低于自我效率评价的情形,即出现同行间的恶意评价。本文将第三方作为间接元素,考虑到这些间接元素在效率评价矩阵中具有传递性,引入间接判断结果对原有的交叉效率矩阵进行反复迭代,并证明迭代过程的最终稳定性。迭代的最终结果可以消除效率矩阵中的恶意评价元素,得到新的效率评价矩阵。最后,通过算例来说明模型的可行性和实用性。

关键词: 效率评价矩阵, 传递闭包矩阵, 模糊算子